One day after a grand jury declined to indict a New York police officer in the death of Eric Garner, prompting angry protests and calls for reform from elected officials, Mayor Bill de Blasio on Thursday announced the start of a significant retraining of the nation’s largest police force.

Mr. de Blasio said the grand jury’s decision had focused the public’s attention on the relationship between the police and the public. “Fundamental questions are being asked, and rightfully so,” he said. “The way we go about policing has to change.”

The de Blasio administration did not immediately explain in detail what the training would entail and how the city would cover the considerable costs of such an undertaking.

Addressing the reaction on Wednesday to the grand jury’s decision, Mr. de Blasio said he understood the frustration of so many and he called on people to channel that anger into working for change.

“People need to know that black lives and brown lives matter as much as white lives,” he said.

Police Commissioner William J. Bratton said the retraining would require some 22,000 officers to complete a three-day course.

The program, beginning this month, is modeled on the periodic required firearms retraining that all officers must regularly undergo. Mr. Bratton first announced the department-wide retraining effort in the wake of Mr. Garner’s death. He provided further details at a City Council hearing in September, including learning “de-escalation” techniques.

On Thursday, First Deputy Benjamin Tucker provided a broad outline of what officers would be taught in each of the three days. The program — which includes teaching on street tactics as well as presenting a “nonjudgmental” posture — was a kind of “refresher” from what officers learn at the Police Academy, Mr. Bratton said.

With many questions about how the grand jury reached its decision, a judge released a few basic details about the proceedings, which by law are carried out in secret. But the records shed little light on the evidence considered by the grand jury and were nothing like what was released after a grand jury in Missouri declined to indict the white police officer who killed Michael Brown.

While the Staten Island district attorney, Daniel M. Donovan Jr., sought the release of the records, according to the judge’s ruling, Mr. Donovan did not ask that transcripts of testimony and exhibits be made public.

In his order, the judge, Stephen J. Rooney, said that the jurors heard from 50 witnesses, 22 of whom were civilians. The rest were police officers, emergency medical personnel and doctors. The jurors also viewed four videos.

President Obama, speaking on Thursday, said that he talked with Mr. de Blasio about what was happening in New York and that he would continue to work with him to shape national reforms. “Too many Americans feel deep unfairness when it comes to the gap between our professed ideals and how laws are applied on a day-to-day basis,” he said.

Gov. Andrew M. Cuomo, speaking in a radio interview, said he would seek a broad review of New York’s criminal justice system, including issues like police training and the grand jury process, in the legislative session that begins in January.

“I think we should look at the whole system,” Mr. Cuomo said on “The Capitol Pressroom.” “This is not just Eric Garner. It’s not just Missouri. It’s bigger and broader.”

But even as protesters promised to take to the streets once again on Thursday night, others faulted the response of elected officials, including Mr. de Blasio, saying they were too critical of the police and could undermine public safety.

Patrick J. Lynch, the president of the Patrolmen’s Benevolent Association, assailed Mr. de Blasio, saying that officers around the city felt he had thrown them “under the bus.” “What we did not hear, is that you cannot resist arrest,” Mr. Lynch said at a news conference.

“We did not hear that that’s why these police officers were at that location that day,” he said. “The community called and complained and said there’s a problem at that location and we were asked to respond.”

“If the mayor wants to change policies and wants us to stand down against crime then say that,” he added. “It’s his policies that we go out and we enforce and the laws of the state of New York.”

When Mr. de Blasio was running for mayor, he promised sweeping reforms of the Police Department and was often scathing in his campaign trail criticism of the department. Those scars have not fully healed, and he is still viewed with suspicion by some in the law enforcement hierarchy.

But while Mr. de Blasio has been calling for reforms since he took office, some felt that action has not been either bold or fast enough.

In one of his first actions as mayor, Mr. de Blasio settled the city’s long-running legal battle over the department’s excessive use of stop-and-frisk tactics and agreed to institute a series of reforms mandated by a federal judge.

At the time, Commissioner Bratton vowed: “We will not break the law to enforce the law. That’s my solemn promise to every New Yorker, regardless of where they were born, where they live, or what they look like.”

One reform ordered by the court was that the city begin a pilot program to outfit officers with body cameras.

The mayor and police commissioner embraced the proposal and even moved to get the pilot running sooner than mandated. Some 60 officers around the city will begin wearing the cameras as soon as Friday, Mr. de Blasio announced this week.

The judge also ordered the appointment of a monitor to develop, in consultation with the parties, widespread reforms of the department’s “policies, training, supervision, monitoring and discipline regarding stop-and-frisk.”

However, legal battles have kept some of the reforms from being instituted and others have been stalled simply because of the difficulty of reforming a department with 35,000 officers.

There has also been concern that any reform might have unintended consequences.

For instance, the police have continued to focus on the kinds of quality-of-life crimes that Mr. Bratton pursued aggressively the first time he was police commissioner in the mid-1990s.

It was the policing of just such a crime that brought Mr. Garner to the attention of the police and led to his death.

The police had been dispatched to the park in Tompkinsville, Staten Island, in response to complaints from residents that people were loitering.

Mr. Garner was a familiar presence in the area and the police confronted him, accusing him of selling individual cigarettes illegally. The rest of the encounter was caught on video, with a white police officer placing him in a chokehold and wrestling him to the ground.

Mr. Garner could be heard pleading, “I can’t breathe.” Several officers then pinned him on the pavement. He died a short time later. His death was ruled a homicide by the city’s medical examiner and was the direct result of the chokehold and the compression of his chest by police officers.

Shortly after the grand jury’s decision in the Garner case on Wednesday, thousands of protesters took to the streets using Mr. Garner’s last words as a rallying cry.

Protesters planned to gather at Foley Square in Lower Manhattan on Thursday night, hoping their voice adds pressure on officials to act. Last night hundreds of people marched to several city landmarks to express their outrage, tying up traffic on the Brooklyn Bridge, forcing the temporary closing of the Lincoln Tunnel, and sprawling across the floor inside Grand Central Terminal at the height of the evening rush.

A group of national civil rights leaders on Thursday announced a “jobs and justice” march in Washington on Dec. 13, part of an effort to form a national movement “committed to forceful change, in peaceful and constructive methods.”

Marc H. Morial, the president and chief executive officer of the National Urban League, called the grand jury’s decision a “travesty of justice.”

“This is a time in this nation, this is a moment, where our consciousness is shocked,” he said.